# Comparing Quantities

## A ratio represents a relation that describes the comparison by division of two quantities of same kind and in the same unit. A percentage is a way of expressing a number as a fraction of 100. ‘Per cent’ means "per hundred". Percentage is denoted by using the percent sign, "%". The percent of a quantity increases or decreases from its original amount is called the percent of change. Discount is a reduction given on marked price. Discount = Marked Price – Sale Price. Discount can be calculated when discount percentage is given. Discount = Discount % of Marked Price Additional expenses made after buying an article are included in the cost price and are known as overhead expenses. C.P. = Buying price + Overhead expenses Whenever the Selling Price is greater than the Cost Price, we earn Profit. If the Cost Price is greater than the Selling Price, we incur Loss. The government charges a tax on the sale of an item. This is called ‘Sales Tax’. Compound interest is the interest calculated on previous year’s amount. Compound Interest = Amount – Principal Amount is calculated as: Amount = P × {1+(r/100)}n Where P = Principal, R = Rate of interest, n = time period (in years) If the cost of a machine depreciates at r% p.a. then its value after n years is given as Cost after n years (A) = P {1 – (r/100)}n Keywords: Value Added Tax (VAT), Simple interest

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• Q1

If a side of a square is increased by 25%, then the area of the square will increase by

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56.25%.

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• Q2

If three numbers are in the ratio of 1:2:3, so that their sum is 504, then the numbers are

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84,168,252.

##### Explanation:

• Q3

If we divide 1458 into two parts, such that their ratio is 2:7, then the antecedent and consequent are

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324 and 1134.

##### Explanation:

• Q4

If the price of an item is reduced by 20%, then in order to restore the original price, the new price must be increased by

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##### Explanation:
• Q5

The ratio of the number of boys and girls in a school is 2:3. If 20% of boys and 30% of girls are scholarship holders, then the percentage of students, who are not scholarship holders, is

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